相关论文: Extremal behavior of squared Bessel processes attr…

We develop classification results for max--stable processes, based on their spectral representations. The structure of max--linear isometries and minimal spectral representations play important roles. We propose a general classification…

We prove that, both for the Brownian snake and for super-Brownian motion in dimension one, the historical path corresponding to the minimal spatial position is a Bessel process of dimension -5. We also discuss a spine decomposition for the…

Flip-flop processes refer to a family of stochastic fluid processes which converge to either a standard Brownian motion (SBM) or to a Markov modulated Brownian motion (MMBM). In recent years, it has been shown that complex distributional…

We study rates of convergence in central limit theorems for the partial sum of squares of general Gaussian sequences, using tools from analysis on Wiener space. No assumption of stationarity, asymptotically or otherwise, is made. The main…

According to the classical theory of Brownian motion, the mean squared displacement of diffusing particles evolves linearly with time whereas the distribution of their displacements is Gaussian. However, recent experiments on mesoscopic…

The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in $n$ fixed points at $n$ fixed past instants. In particular, functional large deviation results are stated for small time. Several…

We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…

We investigate the long-time asymptotic behavior of various entropy measures associated with the Cox-Ingersoll-Ross (CIR) and squared Bessel processes. As the one-dimensional distributions of both processes follow noncentral chi-squared…

Since many environmental processes such as heat waves or precipitation are spatial in extent, it is likely that a single extreme event affects several locations and the areal modeling of extremes is therefore essential if the spatial…

We study the asymptotic behavior of empirical processes generated by measurable bounded functions of an infinite source Poisson transmission process when the session length have infinite variance. In spite of the boundedness of the…

Fractional Brownian motion (FBM), a non-Markovian self-similar Gaussian stochastic process with long-ranged correlations, represents a widely applied, paradigmatic mathematical model of anomalous diffusion. We report the results of…

In this contribution we are concerned with the asymptotic behaviour as $u\to \infty$ of $\mathbb{P}\{\sup_{t\in [0,T]} X_u(t)> u\}$, where $X_u(t),t\in [0,T],u>0$ is a family of centered Gaussian processes with continuous trajectories. A…

Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…

We consider the median of n independent Brownian motions, and show that this process, when properly scaled, converges weakly to a centered Gaussian process. The chief difficulty is establishing tightness, which is proved through direct…

In the article, Besov-Orlicz regularity of sample paths of stochastic processes that are represented by multiple integrals of order $n\in\mathbb{N}$ is treated. We give sufficient conditions for the considered processes to have paths in the…

Two families of stochastic interacting particle systems, the interacting Brownian motions and Bessel processes, are defined as extensions of Dyson's Brownian motion models and the eigenvalue processes of the Wishart and Laguerre processes…

We analyze the tail behavior of the maximum N of Brownian motion minus a parabola and give an asymptotic expansion for P(N>x) as x tends to infinity. This extends a first order result on the tail behavior, which can be deduced from Huesler…

In one-dimensional diffusive processes with discrete steps characterized by geometrically decaying magnitudes, the usual Gaussian broadening familiar from Brownian motion is replaced by bounded probability distributions over particle…

Let $\{X_i,i=1,2,...\}$ be i.i.d. standard gaussian variables. Let $S_n=X_1+...+X_n$ be the sequence of partial sums and $$ L_n=\max_{0\leq i<j\leq n}\frac{S_j-S_i}{\sqrt{j-i}}. $$ We show that the distribution of $L_n$, appropriately…

We prove the convergence of the extremal processes for variable speed branching Brownian motions where the "speed functions", that describe the time-inhomogeneous variance, lie strictly below their concave hull and satisfy a certain weak…